If two events are mutually​ exclusive, why is ​ P(A and B) = 0 ?

Question

A.P (A and B) = 0 because A and B are complements of each other.

B. P (A and B) = 0 because A and B are independent.

C. P ( A and B) = 0 because A and B cannot occur at the same time.

D. P ( A and B) = 0 because A and B each have the same probability.

Answer 1

Hi Autumn,

Think about what “mutually exclusive” means. An example: a road race says that overall placement awards (top 3, etc.) and age group placement awards (top 3 in, for example, 15-19 year old age group) are mutually exclusive. This means that the overall winners do not get age group awards. It goes to the next person in the category. ‘Therefore, your answer ic C. P(A and B)=0 because the events cannot occur at the same time. I hope this helps.